fix(memhub,gzip): 内存池 OOM 归属画像与 free 拒绝现场；gzip 注解 *= 词法粘连
memhub: alloc 失败打印归属 site/ctx 与存活块 order 分布（新增 dump_alive_orders）；free 被 _is_valid_ptr 拒绝时首次打印现场；接通 big_alloc_count gzip: ub: uchar*= buf 补空格（*= 被词法合并为单 OP，注解止于 uchar） 新增 traceback 模块；删除 dbgstack.vp；其余模块随新语法与尺寸口径同步
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@@ -7,8 +7,9 @@
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# * Scope and feature set:
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# * - Fundamental mathematical constants: π, e, π/2, π/4, reciprocal π, 2/π, ln(2), ln(10), 2/sqrt(π), DBL_MAX.
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# * - Angle conversion: radians ↔ degrees helpers.
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# * - Trigonometric functions: sin, cos, tan, sinf, cosf, tanf. Argument reduction is performed using subtraction of
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# * 2π until the value falls into [-π, π]; polynomial approximations are truncated series tuned for the target interval.
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# * - Trigonometric functions: sin, cos, tan, sinf, cosf, tanf. Argument reduction is O(1): a three-constant
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# * Cody-Waite step for |x| < 2^20, and a Payne-Hanek step (20-word table of 2/π) above. Both yield r ∈ [-π/4, π/4]
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# * as a double-double fed to the truncated Taylor series.
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# * - Inverse trigonometric functions: asin, acos, atan, atan2. asin uses a minimax polynomial suitable for [-1, 1];
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# * atan relies on a Taylor core limited to |x| ≤ 1 combined with range folding via reciprocal and quadrant logic.
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# * - Hyperbolic trigonometry: sinh, cosh, tanh, built atop exp and exp(-x).
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@@ -69,30 +70,33 @@ define U_M_2_SQRT_PI: double = 1.77245385090551602730
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define DBL_MAX: double = 1.7976931348623157e308
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define NEG_1E308: double = -1e308
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# Argument reduction constants for sin/cos/tan: pi/2 split into HI+MID+LO and 2/pi (all exact doubles),
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# plus the 2^20 limit below which Cody-Waite applies (so each fn*HK product stays exact in 53 bits).
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define U_M_PIO2_HI: double = 1.57079632673412561417e+00
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define U_M_PIO2_MID: double = 6.07710050650619224932e-11
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define U_M_PIO2_LO: double = 3.52155986518320018165e-27
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define U_M_INV_PIO2: double = 6.36619772367581382433e-01
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define U_M_REDUCE_LIMIT: double = 1048576.0
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def radians(degrees: double) -> double: return degrees * (U_M_PI / 180.0)
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def degrees(radians: double) -> double: return radians * (180.0 / U_M_PI)
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def sin(x: double) -> double:
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while x > U_M_PI:
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x -= 2.0 * U_M_PI
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while x < -U_M_PI:
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x += 2.0 * U_M_PI
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def _sin_core(x: double) -> double:
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"""sin(r) Taylor series, 8 terms, valid on |r| <= pi/4."""
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x2: double = x * x
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result: double = x
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term: double = x
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coeffs: const [8]double = [6.0, 20.0, 42.0, 72.0, 110.0, 156.0, 210.0, 272.0]
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sign: double = -1.0
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coeffs: const [8]double = [6.0, 20.0, 42.0, 72.0, 110.0, 156.0, 210.0, 272.0]
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for c in coeffs:
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term = term * x2 / c
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result += sign * term
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sign = -sign
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return result
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def cos(x: double) -> double:
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while x > U_M_PI:
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x -= 2.0 * U_M_PI
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while x < -U_M_PI:
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x += 2.0 * U_M_PI
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def _cos_core(x: double) -> double:
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"""cos(r) Taylor series, 8 terms, valid on |r| <= pi/4."""
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x2: double = x * x
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result: double = 1.0
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term: double = 1.0
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@@ -104,6 +108,154 @@ def cos(x: double) -> double:
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sign = -sign
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return result
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def _mul_add(a: uint64, b: uint64, c: uint64, lo: rawptr[uint64], hi: rawptr[uint64]):
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"""Write (hi:lo) = a*b + c using 32-bit limbs for the full 128-bit product."""
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a0: uint64 = a & 0xFFFFFFFF
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a1: uint64 = a >> 32
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b0: uint64 = b & 0xFFFFFFFF
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b1: uint64 = b >> 32
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w0: uint64 = a0 * b0
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t: uint64 = a1 * b0 + (w0 >> 32)
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w1: uint64 = t & 0xFFFFFFFF
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w2: uint64 = t >> 32
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w1 = a0 * b1 + w1
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h: uint64 = a1 * b1 + w2 + (w1 >> 32)
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l: uint64 = (w1 << 32) | (w0 & 0xFFFFFFFF)
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l2: uint64 = l + c
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if l2 < l: h = h + 1
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*lo = l2
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*hi = h
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def _two_prod(a: double, b: double, ph: rawptr[double], pl: rawptr[double]):
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"""Write a*b as the exact double-double (ph + pl) via Dekker splitting (no FMA required)."""
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split: double = 134217729.0
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p: double = a * b
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ca: double = split * a
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ahi: double = ca - (ca - a)
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alo: double = a - ahi
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cb: double = split * b
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bhi: double = cb - (cb - b)
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blo: double = b - bhi
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*ph = p
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*pl = ((ahi * bhi - p) + ahi * blo + alo * bhi) + alo * blo
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def _rem_pio2(x: double, rh: rawptr[double], rl: rawptr[double]) -> int:
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"""O(1) reduction of finite x >= 0: x = n*(pi/2) + r with |r| <= pi/4; returns n mod 4, writes r = rh + rl."""
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if x < U_M_REDUCE_LIMIT:
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# Cody-Waite three-step with pi/2 = HI + MID + LO; each fn*HK product is exact for fn < 2^20
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q: double = x * U_M_INV_PIO2
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k: int = int(q)
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if q - double(k) > 0.5: k = k + 1
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fn: double = double(k)
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r: double = x - fn * U_M_PIO2_HI
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w1: double = fn * U_M_PIO2_MID
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y0: double = r - w1
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w2: double = fn * U_M_PIO2_LO
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rhv: double = y0 - w2
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*rh = rhv
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*rl = ((r - y0) - w1) + ((y0 - rhv) - w2)
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return k & 3
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# Payne-Hanek: a 20-word (1280-bit) 2/pi table; multiply the 53-bit mantissa and read off the fraction
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twopi: const [20]uint64 = [
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0xA2F9836E4E441529, 0xFC2757D1F534DDC0, 0xDB6295993C439041, 0xFE5163ABDEBBC561,
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0xB7246E3A424DD2E0, 0x06492EEA09D1921C, 0xFE1DEB1CB129A73E, 0xE88235F52EBB4484,
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0xE99C7026B45F7E41, 0x3991D639835339F4, 0x9C845F8BBDF9283B, 0x1FF897FFDE05980F,
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0xEF2F118B5A0A6D1F, 0x6D367ECF27CB09B7, 0x4F463F669E5FEA2D, 0x7527BAC7EBE5F17B,
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0x3D0739F78A5292EA, 0x6BFB5FB11F8D5D08, 0x56033046FC7B6BAB, 0xF0CFBC209AF4361D
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]
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xv: double = x
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xb: uint64 = 0
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*&xb = *&xv
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ef: uint64 = (xb >> 52) & 0x7FF
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m: uint64 = (xb & 0xFFFFFFFFFFFFF) | 0x10000000000000
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e: int = int(ef) - 1075
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shift: int = 1280 - e
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qw: int = shift >> 6
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s: int = shift & 63
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b: [21]uint64
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carry: uint64 = 0
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for j in range(20):
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lo: uint64 = 0
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hi: uint64 = 0
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_mul_add(m, twopi[19 - j], carry, &lo, &hi)
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b[j] = lo
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carry = hi
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b[20] = carry
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lo2: uint64 = b[qw] >> s
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if s == 63: lo2 = (b[qw] >> 63) | (b[qw + 1] << 1)
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k: int = int(lo2 & 3)
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a1: uint64 = b[qw] & ((uint64(1) << s) - 1)
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a2: uint64 = b[qw - 1]
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a3: uint64 = b[qw - 2]
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fhi: uint64 = a2
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flo: uint64 = a3
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if s != 0:
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sh: int = 64 - s
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fhi = (a1 << sh) | (a2 >> s)
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flo = (a2 << sh) | (a3 >> s)
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# fractional part f = fhi*2^-64 + flo*2^-128; split off the top 53 bits so df is exact
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f53: uint64 = fhi >> 11
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df: double = double(f53)
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de: double = double(fhi - (f53 << 11))
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fh: double = df * 1.1102230246251565e-16
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fl: double = de * 5.421010862427522e-20 + double(flo) * 2.9387358770557188e-39
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r0h: double = fh
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r0l: double = fl
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n: int = k
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if fh > 0.5 or (fh == 0.5 and fl > 0.0):
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n = (k + 1) & 3
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r0h = fh - 1.0
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ph: double = 0.0
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pl: double = 0.0
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_two_prod(r0h, U_M_PIO2_HI, &ph, &pl)
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*rh = ph
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*rl = pl + r0h * U_M_PIO2_MID + r0h * U_M_PIO2_LO + r0l * U_M_PIO2_HI
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return n
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def sin(x: double) -> double:
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u: uint64 = 0
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xv: double = x
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*&u = *&xv
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ef: uint64 = (u >> 52) & 0x7FF
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if ef == 0x7FF: return x - x # inf/nan -> NaN
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neg: int = int(u >> 63)
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ax: double = x if neg == 0 else -x
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rh: double = 0.0
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rl: double = 0.0
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n: int = _rem_pio2(ax, &rh, &rl)
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sr: double = _sin_core(rh) + _cos_core(rh) * rl
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cr: double = _cos_core(rh) - _sin_core(rh) * rl
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res: double = 0.0
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if n == 0: res = sr
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elif n == 1: res = cr
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elif n == 2: res = -sr
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else: res = -cr
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return -res if neg != 0 else res
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def cos(x: double) -> double:
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u: uint64 = 0
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xv: double = x
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*&u = *&xv
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ef: uint64 = (u >> 52) & 0x7FF
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if ef == 0x7FF: return x - x # inf/nan -> NaN
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neg: int = int(u >> 63)
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ax: double = x if neg == 0 else -x
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rh: double = 0.0
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rl: double = 0.0
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n: int = _rem_pio2(ax, &rh, &rl)
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sr: double = _sin_core(rh) + _cos_core(rh) * rl
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cr: double = _cos_core(rh) - _sin_core(rh) * rl
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if n == 0: return cr
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elif n == 1: return -sr
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elif n == 2: return -cr
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else: return sr
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def tan(x: double) -> double: return sin(x) / cos(x)
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@@ -364,38 +516,8 @@ def sqrtf(x: float) -> float:
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guess = (guess + x / guess) / 2.0
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return guess
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def sinf(x: float) -> float:
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while x > 3.14159265:
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x -= 6.28318530
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while x < -3.14159265:
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x += 6.28318530
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x2: float = x * x
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result: float = x
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term: float = x
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sign: float = -1.0
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coeffs: const [8]float = [6.0, 20.0, 42.0, 72.0, 110.0, 156.0, 210.0, 272.0]
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for c in coeffs:
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term = term * x2 / c
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result += sign * term
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sign = -sign
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return result
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def cosf(x: float) -> float:
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while x > 3.14159265:
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x -= 6.28318530
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while x < -3.14159265:
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x += 6.28318530
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x2: float = x * x
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result: float = 1.0
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term: float = 1.0
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sign: float = -1.0
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coeffs: const [8]float = [2.0, 12.0, 30.0, 56.0, 90.0, 132.0, 182.0, 240.0]
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for c in coeffs:
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term = term * x2 / c
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result += sign * term
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sign = -sign
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return result
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def sinf(x: float) -> float: return float(sin(double(x)))
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def cosf(x: float) -> float: return float(cos(double(x)))
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def tanf(x: float) -> float:
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c: float = cosf(x)
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